## Geometry & Topology

### The Gromov width of $4$–dimensional tori

#### Abstract

Let $ω$ be any linear symplectic form on the $4$–torus $T4$. We show that in all cases $(T4,ω)$ can be fully filled by one symplectic ball. If $(T4,ω)$ is not symplectomorphic to a product $T2(μ)×T2(μ)$ of equal sized factors, then it can also be fully filled by any finite collection of balls provided only that their total volume is less than that of $(T4,ω)$.

#### Article information

Source
Geom. Topol., Volume 17, Number 5 (2013), 2813-2853.

Dates
Accepted: 13 June 2013
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732688

Digital Object Identifier
doi:10.2140/gt.2013.17.2813

Mathematical Reviews number (MathSciNet)
MR3190299

Zentralblatt MATH identifier
1277.57024

#### Citation

Latschev, Janko; McDuff, Dusa; Schlenk, Felix. The Gromov width of $4$–dimensional tori. Geom. Topol. 17 (2013), no. 5, 2813--2853. doi:10.2140/gt.2013.17.2813. https://projecteuclid.org/euclid.gt/1513732688

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